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Full text of "Analytical Mechanics"

MOTION 91 It must be remembered that dv is the vector difference of the velocities at the beginning and at the end of the interval of time dt] therefore f is a vector magnitude with a direction which is, in general, different from that of the velocity. 87. Dimensions and Units of Acceleration. — The dimensions of acceleration are [LT~~2]. The unit of acceleration is a unit change in the velocity per second. Therefore the C.G.S. unit is ——----- or ----'-. Thus if the velocity of a sec. sec.~ particle increases by an amount of one —- during each sec. second it has a unit acceleration. The engineering unit of acceleration is the foot per sec. per sec., —'—• PROBLEMS. 1. Express the engineering unit of acceleration in terms of the C.G.S. unit. 2. Taking the value of the gravitational acceleration to be 980 -^^ > fi ,.. , . ft. , miles sec- find its value in----- and -—— • sec.2 hr.2 3. A train moving at the rate of 30 kilometers per hour is brought to rest in two minutes. Find the average acceleration and express it in , - cm. ft. j km. terms of----- >----- and -—- • sec.2 sec.2 hr.2 88. Components of Acceleration along Rectangular Axes. — Suppose a particle*to describe a path in the xy-plane. Then if YI and v2 be the velocities at two neighboring points, we can write = (x2 + £2) — (xi + yi) = dx+dy. x _ dv = dx dy dt dt dt But since f = f * + f y, r , x _ dX.1 li dt dt